Séminaire d'arithmétique à Lyon

# Algebraic Brauer groups modulo constants of homogeneous spaces

## by Manh Linh Nguyen

Europe/Paris
M7.411 (ENS Lyon, UMPA)

### M7.411

#### ENS Lyon, UMPA

Description

For a homogeneous space of a semisimple, simply connected linear algebraic group, the quotient of its "unramified algebraic" Brauer group by its subgroup of constants injects into a certain subgroup of the first Galois cohomology of its geometric Picard group. This inclusion is an isomorphism if either the homogeneous space has a rational point or the third Galois cohomology of the multiplicative group over the base field vanishes. In my talk, I construct an example where this inclusion is strict. This is the text https://arxiv.org/abs/2204.10967.